Next, we consider  a clustering -based downsampling approach, known as  the \(k\) -means algorithm [1]}.  It is a well-known unsupervised learning algorithm that groups similar data into clusters. Using this, we partition the original data set \(\mathcal {D}\)  into several clusters and only use the sampled data associated with the  closest cluster  to the new data \(\tilde{y}^n_k\)  in the constraints described in Remark REF . Further,  to address the potentially poor over-approximation near the boundaries of the cluster, one additional random data point  is picked from each  of the other cluster s. The scalability of this method is better than the grid -based method, since the number of regions depends only on the number of clusters.  However, computing the clusters might be computationally  expensive.
